All of these terms, and some others, have been used in The New York Times to describe a person who has entered, lived in or worked in the United States without proper authorization — and each has been met with criticism.

In fact, an ambitious and comprehensive portrait of the 11 million unauthorized immigrants in the United States that was published in Tuesday’s paper drew objections for both its use of “illegal immigrants” in the headline (which some saw as partisan and offensive) and its reference within the article to “undocumented immigrants” (which others saw as overly sympathetic).

In a debate as contentious as the one surrounding immigration policy in the United States, where even the most basic terminology is fraught with political implications, how do Times journalists decide, in a given instance, which term to employ?

Vivian Yee, a national immigration correspondent, grapples with the question on a regular basis — and acknowledged that readers’ reactions tend to break predictably along political lines. Conservatives, she said, often insist on using the term “illegal immigrants,” while liberals tend to push for “undocumented immigrants.”

The article on Tuesday, which Ms. Yee helped to report, offered one example of how The Times attempts to navigate this linguistic quandary.

“We decided that a story written with the intention of explaining the starting points of the immigration debate shouldn’t take sides on the semantics of the debate,” Ms. Yee said in an email, explaining that the article deliberately included a mix of different terms: “illegal,” “undocumented,” and “unauthorized.”

“And, of course,” she added, “we tried to show that there are real, live human faces to the issue by telling a few of their stories.”

The Times’s style guide, a 368-page reference manual that offers guidance on everything from grammar and punctuation to particularly thorny issues of usage, acknowledges that the term “illegal immigrant” may be considered “loaded or offensive” by some readers. “Without taking sides or resorting to euphemism,” the guide states, “consider alternatives when appropriate to explain the specific circumstances of the person in question or to focus on actions: who crossed the border illegally; who overstayed a visa; who is not authorized to work in this country.”

“Unauthorized” and “undocumented” are also listed as acceptable descriptions, though each is presented with caveats. “Undocumented is the term preferred by many immigrants and their advocates, but it has a flavor of euphemism and should be used with caution outside quotation,” the guide states. And “unauthorized,” it warns, has a “bureaucratic tone.”

Off the table entirely are “illegal,” when used as a noun, and the sinister-sounding “alien.”

Of course, employing the right language is only part of the difficulty of reporting on immigration: Finding individual immigrants who will agree to have their names and, in some cases, their photographs published in The Times can also prove particularly challenging.

“It’s extraordinarily more difficult now than it used to be,” said Jennifer Medina, a correspondent who contributed reporting to Tuesday’s article, when asked about her process for convincing immigrants, regardless of their legal status, to speak on the record about their experiences. “People are much more fearful about repercussions, about outing themselves, about drawing any sort of attention to themselves. There’s a pervasive sense of fear.”

That fear is largely a result of a sea change in immigration policy under the new administration. (Another result of President Trump’s approach — its effect on refugees from Central America who had applied, under the Obama administration, for sanctuary in the United States — was explored in Thursday’s front-page article filed from San Salvador.)

But the argument to convince vulnerable immigrants to share their stories is always the same, Ms. Medina said: “By talking about what you’re going through, you’re giving voice to a group that otherwise might not be heard from.”

“And,” she added, “if you don’t talk about your experience, nobody is going to talk about it for you.”